Answer: Increase probability of down movement, (d), by about 3.57% percentage points

## Explanation In the binomial model, the risk-neutral probability of an up movement (p) is calculated as: $$p = \frac{e^{(r-q)\Delta t} - d}{u - d}$$ Where: - r = risk-free rate (4.0%) - q = continuous dividend yield (2.0%) - Δt = time step (1 year) - u = up movement factor - d = down movement factor **Without dividend (q = 0%):** - Given p = 0.50 - This implies: $e^{r\Delta t} - d = 0.50(u - d)$ - Since u = 1/d in a standard binomial model, and with p = 0.50, we have symmetric probabilities **With dividend (q = 2.0%):** The new risk-neutral probability becomes: $$p_{new} = \frac{e^{(0.04-0.02) \times 1} - d}{u - d} = \frac{e^{0.02} - d}{u - d}$$ Since $e^{0.02} ≈ 1.0202$ is smaller than $e^{0.04} ≈ 1.0408$, the numerator decreases, which means: - p decreases (probability of up movement decreases) - d = 1 - p increases (probability of down movement increases) The exact change can be calculated as approximately 3.57% percentage points increase in the down probability. Therefore, including the 2.0% dividend yield increases the probability of a down movement by about 3.57 percentage points.

Author: LeetQuiz .